In this section, we first give a brief overview of the existing approximation strategies for the PSD cone \(\mathbb {S}^n_+\) , including (scaled-) diagonally dominant matrices [1]} and their block extensions [2]}. These approximation strategies have shown promising computational efficiency improvement to solve (REF )-(REF ), but may also suffer from conservatism in solution quality [2]}, [4]}. We then present the problem statement of improving the approximation quality via iterative algorithms.
